**299,99 zł**

- Wydawca: Wiley-VCH
- Kategoria: Nauka i nowe technologie
- Język: angielski
- Rok wydania: 2015

Completely revised, updated, and enlarged, this second edition now contains a subchapter on biorecognition assays, plus a chapter on bioprocess control added by the new co-author Jun-ichi Horiuchi, who is one of the leading experts in the field.
The central theme of the textbook remains the application of chemical engineering principles to biological processes in general, demonstrating how a chemical engineer would address and solve problems. To create a logical and clear structure, the book is divided into three parts. The first deals with the basic concepts and principles of chemical engineering and can be read by those students with no prior knowledge of chemical engineering. The second part focuses on process aspects, such as heat and mass transfer, bioreactors, and separation methods. Finally, the third section describes practical aspects, including medical device production, downstream operations, and fermenter engineering. More than 40 exemplary solved exercises facilitate understanding of the complex engineering background, while self-study is supported by the inclusion of over 80 exercises at the end of each chapter, which are supplemented by the corresponding solutions.
An excellent, comprehensive introduction to the principles of **Biochemical Engineering**.

Ebooka przeczytasz w aplikacjach Legimi na:

Liczba stron: 488

Cover

Related Titles

Title Page

Copyright

Preface to the Second Edition

Preface to the First Edition

About the companion website

Nomenclature

Part I: Basic Concepts and Principles

Chapter 1: Introduction

1.1 Background and Scope

1.2 Dimensions and Units

1.3 Intensive and Extensive Properties

1.4 Equilibria and Rates

1.5 Batch Versus Continuous Operation

1.6 Material Balance

1.7 Energy Balance

Chapter 2: Elements of Physical Transfer Processes

2.1 Introduction

2.2 Heat Conduction and Molecular Diffusion

2.3 Fluid Flow and Momentum Transfer

2.4 Laminar Versus Turbulent Flow

2.5 Transfer Phenomena in Turbulent Flow

2.6 Film Coefficients of Heat and Mass Transfer

Chapter 3: Chemical and Biochemical Kinetics

3.1 Introduction

3.2 Fundamental Reaction Kinetics

Chapter 4: Cell Kinetics

4.1 Introduction

4.2 Cell Growth

4.3 Growth Phases in Batch Culture

4.4 Factors Affecting Rates of Cell Growth

4.5 Cell Growth in Batch Fermentors and Continuous Stirred-Tank Fermentors (CSTF)

Part II: Unit Operations and Apparatus for Biosystems

Chapter 5: Heat Transfer

5.1 Introduction

5.2 Overall Coefficients

U

and Film Coefficients

h

5.3 Mean Temperature Difference

5.4 Estimation of Film Coefficients

h

5.5 Estimation of Overall Coefficients

U

Chapter 6: Mass Transfer

6.1 Introduction

6.2 Overall Coefficients

K

and Film Coefficients

k

of Mass Transfer

6.3 Types of Mass Transfer Equipment

6.4 Models for Mass Transfer at the Interface

6.5 Liquid Phase Mass Transfer with Chemical Reactions

6.6 Correlations for Film Coefficients of Mass Transfer

6.7 Performance of Packed Column

Chapter 7: Bioreactors

7.1 Introduction

7.2 Some Fundamental Concepts

7.3 Bubbling Gas–Liquid Reactors

7.4 Mechanically Stirred Tanks

7.5 Gas Dispersion in Stirred Tanks

7.6 Bubble Columns

7.7 Airlift Reactors

7.8 Packed-Bed Reactors

7.9 Microreactors

Chapter 8: Membrane Processes

8.1 Introduction

8.2 Dialysis

8.3 Ultrafiltration

8.4 Microfiltration

8.5 Reverse Osmosis

8.6 Membrane Modules

Chapter 9: Cell–Liquid Separation and Cell Disruption

9.1 Introduction

9.2 Conventional Filtration

9.3 Microfiltration

9.4 Centrifugation

9.5 Cell Disruption

Chapter 10: Sterilization

10.1 Introduction

10.2 Kinetics of Thermal Death of Cells

10.3 Batch Heat Sterilization of Culture Media

10.4 Continuous Heat Sterilization of Culture Media

10.5 Sterilizing Filtration

Chapter 11: Adsorption and Chromatography

11.1 Introduction

11.2 Equilibria in Adsorption

11.3 Rates of Adsorption into Adsorbent Particles

11.4 Single- and Multistage Operations for Adsorption

11.5 Adsorption in Fixed Beds

11.6 Separation by Chromatography

11.7 Biorecognition Assay

Part III: Practical Aspects in Bioengineering

Chapter 12: Fermentor Engineering

12.1 Introduction

12.2 Stirrer Power Requirements for Non-Newtonian Liquids

12.3 Heat Transfer in Fermentors

12.4 Gas–Liquid Mass Transfer in Fermentors

12.5 Criteria for Scaling-Up Fermentors

12.6 Modes of Fermentor Operation

12.7 Fermentors for Animal Cell Culture

Chapter 13: Instrumentation and Control of Bioprocesses

13.1 Introduction

13.2 Instrumentation of Bioprocesses

13.3 Control of Bioprocesses

13.4 Advanced Control of Bioprocesses

Chapter 14: Downstream Operations in Bioprocesses

14.1 Introduction

14.2 Separation of Microorganisms by Filtration and Microfiltration

14.3 Separation by Chromatography

14.4 Separation in Fixed-Beds

14.5 Sanitation in Downstream Processes

Chapter 15: Medical Devices

15.1 Introduction

15.2 Blood and Its Circulation

15.3 Oxygenation of Blood

15.4 Artificial Kidney

15.5 Bioartificial Liver

References

Appendix A: Conversion Factors for Units

Appendix B: Solutions to the Problems

Index

EULA

XIII

XIV

XV

XVII

XIX

XX

XXI

XXII

3

4

5

6

7

8

9

10

11

12

155

156

157

158

159

160

161

162

163

164

165

166

167

168

169

170

171

172

173

174

175

176

177

178

179

180

181

182

183

184

185

186

187

191

192

193

194

195

196

197

198

199

200

201

202

203

204

205

206

207

208

209

210

211

212

213

214

215

217

218

219

220

221

222

223

224

225

226

227

228

229

230

231

232

233

234

235

236

237

238

239

240

241

242

243

244

245

246

247

248

249

251

252

253

254

255

256

257

258

259

260

261

262

263

264

265

266

267

268

269

270

271

272

273

274

275

276

277

278

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

47

48

49

50

51

52

53

54

55

56

59

60

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

91

92

93

94

95

97

98

99

100

101

102

103

104

105

106

107

108

109

110

111

112

113

114

115

116

117

118

119

120

121

122

123

124

125

126

127

128

129

130

131

132

133

134

135

136

137

138

139

140

141

142

143

145

146

147

148

149

150

151

152

153

1

57

189

279

280

281

282

283

284

285

286

287

288

289

290

291

292

293

294

Cover

Table of Contents

Preface to the Second Edition

Preface to the First Edition

Part I: Basic Concepts and Principles

Chapter 1: Introduction

Figure 2.1

Figure 2.2

Figure 2.3

Figure 2.4

Figure 2.5

Figure 3.1

Figure 3.2

Figure 3.3

Figure 3.4

Figure 3.5

Figure 3.6

Figure 3.7

Figure 3.8

Figure 3.9

Figure 4.1

Figure 4.2

Figure 4.3

Figure 4.4

Figure 5.1

Figure 5.2

Figure 5.3

Figure 6.1

Figure 6.2

Figure 6.3

Figure 6.4

Figure 6.5

Figure 7.1

Figure 7.2

Figure 7.3

Figure 7.4

Figure 7.5

Figure 7.6

Figure 7.7

Figure 7.8

Figure 7.9

Figure 7.10

Figure 7.11

Figure 7.12

Figure P7.6

Figure 8.1

Figure 8.2

Figure 8.3

Figure 8.4

Figure 9.1

Figure 9.2

Figure 9.3

Figure 10.1

Figure 10.2

Figure 10.3

Figure 10.4

Figure 10.5

Figure 10.6

Figure 11.1

Figure 11.2

Figure 11.3

Figure 11.4

Figure 11.5

Figure 11.6

Figure 11.10

Figure 11.11

Figure 11.12

Figure 11.13

Figure 12.1

Figure 12.2

Figure 12.3

Figure 12.4

Figure 13.1

Figure 13.2

Figure 13.3

Figure 13.4

Figure 13.5

Figure 13.6

Figure 14.1

Figure 14.2

Figure 14.3

Figure 14.4

Figure 14.5

Figure 14.6

Figure 14.7

Figure 14.8

Figure 15.1

Figure 15.2

Figure 15.3

Figure 15.4

Figure 15.5

Table P2.2

Table 3.1

Table 3.2

Table 3.3

Table P3.1

Table P3.2

Table P3.4

Table P3.6

Table P3.7

Table P3.8

Table P3.9

Table 4.1

Table 4.3

Table 4.4

Table P4.3

Table P4.4

Table 5.1

Table 6.1

Table P6.1

Table 7.1

Table P8.1

Table 9.1

Table P9.2

Table 10.1

Table 11.1

Table 13.1

Table 13.2

Table 13.3

Table 13.4

Table 15.1

Hill, C.G., Root, T.W.

Introduction to Chemical Engineering Kinetics & Reactor Design

Second Edition

2014

Print ISBN: 978-1-118-36825-1; also available in electronic formats

Soetaert, W., Vandamme, E.J. (eds.)

Industrial Biotechnology

Sustainable Growth and Economic Success

2010

Print ISBN: 978-3-527-31442-3; also available in electronic formats

Wiley-VCH (ed.)

Ullmann's Biotechnology and Biochemical Engineering

2 Volume Set

2007

Print ISBN: 978-3-527-31603-8

Buchholz, K., Collins, J.

Concepts in Biotechnology

History, Science and Business

2010

Print ISBN: 978-3-527-31766-0

Buchholz, K., Kasche, V., Bornscheuer, U.T.

Biocatalysts and Enzyme Technology

2nd Edition

2012

Print ISBN: 978-3-527-32989-2; also available in electronic formats

Wiley-VCH (ed.)

Ullmann's Reaction Engineering

2 Volume Set

2013

Print ISBN: 978-3-527-33371-4

Buzzi-Ferraris, G./Manenti, F.

Fundamentals and Linear Algebra for the Chemical Engineer

Solving Numerical Problems

2010

Print ISBN: 978-3-527-32552-8

Interpolation and Regression Models for the Chemical Engineer

Solving Numerical Problems

2010

Print ISBN: 978-3-527-32652-5

Nonlinear Systems and Optimization for the Chemical Engineer

Solving Numerical Problems

2013

Print ISBN: 978-3-527-33274-8; also available in electronic formats

Differential and Differential-Algebraic Systems for the Chemical Engineer

Solving Numerical Problems

2014

Print ISBN: 978-3-527-33275-5; also available in electronic formats

Shigeo Katoh, Jun-ichi Horiuchi, and Fumitake Yoshida

The Authors

Dr. Shigeo Katoh

Kobe University

Graduate School of Science and Technology

Kobe 657-8501

Japan

Prof. Jun-ichi Horiuchi

Kitami Institute of Technology

Biotechnology & Environmental Chemistry

Koen-cho 165

Kitami

Hokkaido

Japan

Fumitake Yoshida

Formerly Kyoto University, Japan

Sakyo-ku Matsugasaki

Yobikaeshi-cho 2

Kyoto 606-0912

Japan

All books published by Wiley-VCH are carefully produced. Nevertheless, authors, editors, and publisher do not warrant the information contained in these books, including this book, to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate.

Library of Congress Card No.: applied for

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The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the Internet at < http://dnb.d-nb.de>.

© 2015 Wiley-VCH Verlag GmbH & Co. KGaA,

Boschstr. 12, 69469 Weinheim, Germany

All rights reserved (including those of translation into other languages). No part of this book may be reproduced in any form – by photoprinting, microfilm, or any other means – nor transmitted or translated into a machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not specifically marked as such, are not to be considered unprotected by law.

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Bioengineering can be defined as the application of the various branches of engineering, including mechanical, electrical, and chemical engineering, to biological systems, including those related to medicine. Likewise, biochemical engineering refers to the application of chemical engineering to biological systems. This book is intended for use by undergraduates, and deals with the applications of chemical engineering to biological systems in general. In that respect, no preliminary knowledge of chemical engineering is assumed.

In the first edition of Biochemical Engineering, published in 2009, we attempted to demonstrate how a typical chemical engineer would address and solve such problems in order to facilitate an understanding by newcomers to this field of study. In Part I of the book, we outlined some very elementary concepts of chemical engineering for those new to the field, and in Part II, “Unit operations and apparatus for bio-systems” were covered. Although in Part III we described applications of biochemical engineering to bioprocesses and to other areas, this part did not include a chapter for “Bioprocess control.” In bioindustry processes, the control of bioreactors is essential for the production of high-quality products under validated conditions. A fundamental understanding of process control should be very useful for all biochemical engineers, as well as for chemical engineers. Thus, we welcome a new coauthor, Prof. Jun-ichi Horiuchi, who is a leading researcher in the Department of Biotechnology and Environmental Chemistry, Kitami Institute of Technology.

Currently, many biopharmaceuticals, which are proteins in many cases, are produced in many bioindustry fields, and the measuring of the concentrations and bioactivities of these products is thus becoming essential in bioindustry. We have added a new section for “Biorecognition assay” in Chapter 11, and we explain the fundamental aspects of biorecognition and its application for the measurement of bioproducts at low concentrations. In this edition, we have included some examples and some new problems to assist in the progress with learning how to solve problem.

We would like to express great thanks to Prof. Michimasa Kishimoto and Prof. Yoichi Kumada for their useful discussion, particularly for Chapters 11–13. We also thank the external reviewers for providing invaluable suggestions and the staffs of Wiley-VCH Verlag for planning, editing, and producing this second edition.

Shigeo Katoh

Bioengineering can be defined as the application of the various branches of engineering, including mechanical, electrical, and chemical engineering, to biological systems, including those related to medicine. Likewise, biochemical engineering refers to the application of chemical engineering to biological systems. This book is intended for use by undergraduates, and deals with the applications of chemical engineering to biological systems in general. In that respect, no preliminary knowledge of chemical engineering is assumed.

Since the publication of the pioneering text Biochemical Engineering, by Aiba, Humphrey, and Millis in 1964, several articles on the so-called “biochemical” or “bioprocess” engineering have been published. While all of these have combined the applications of chemical engineering and biochemistry, the relative space allocated to the two disciplines has varied widely among the different texts.

In this book, we describe the application of chemical engineering principles to biological systems, but in doing so assume that the reader has some practical knowledge of biotechnology, but no prior background in chemical engineering. Hence, we have attempted to demonstrate how a typical chemical engineer would address and solve such problems. Consequently, a simplified rather than rigorous approach has often been adopted in order to facilitate an understanding by newcomers to this field of study. Although in Part I of the book we have outlined some very elementary concepts of chemical engineering for those new to the field, the book can be used equally well for senior or even postgraduate level courses in chemical engineering for students of biotechnology, when the reader can simply start from Part II. Naturally, this book should prove especially useful for those biotechnologists interested in self-studying chemical bioengineering. In Part III, we provide descriptions of the applications of biochemical engineering not only to bioprocessing but also to other areas, including the design of selected medical devices. Moreover, to assist progress in learning, a number of worked examples, together with some “homework” problems, are included in each chapter.

I would like to thank the two external reviewers, Prof. Ulfert Onken (Dortmund University) and Prof. Alois Jungbauer (University of Natural Resources and Applied Life Sciences), for providing invaluable suggestions. I also thank the staff of Wiley-VCH Verlag for planning, editing, and producing this book. Finally I thank Kyoko, my wife, for her support while I was writing this book.

This book is accompanied by a companion website:

http://www.wiley.com/go/katoh/biochem_eng_e2

The website includes detailed solutions to the problems in the book.

(Some symbols and subscripts explained in the text are omitted.)

A

area (m

2

)

a

specific interfacial area (m

2

m

−3

or m

−1

)

b

width of rectangular conduit (m)

C

concentration (kg or kmol m

−3

, g or mol cm

−3

)

C

n

cell number density (m

−3

)

C

p

heat capacity (kcal °C

−1

or kJ K

−1

)

Cl

clearance of kidney or hemodialyzer (cm

3

min

−1

)

c

p

specific heat capacity (kJ kg

−1

K

−1

or kcal kg

−1

°C

−1

)

D

diffusivity (m

2

h

−1

or cm

2

s

−1

)

D

tank or column diameter (m)

Dl

dialysance of hemodialyzer (cm

3

min

−1

)

d

diameter (m or cm)

d

e

equivalent diameter (m or cm)

E

enhancement factor =

k

*/

k

(−)

E

internal energy (kJ)

E

a

activation energy (kJ kmol

−1

)

E

D

,

E

H

,

E

V

eddy diffusivity, eddy thermal diffusivity, and eddy kinematic viscosity, respectively (m

2

h

−1

or cm

2

s

−1

)

E

f

effectiveness factor (−)

F

volumetric flow rate (m

3

h

−1

or cm

3

s

−1

or min

−1

)

f

friction factor

G

m

fluid mass velocity (kg h

−1

m

−2

)

G

V

volumetric gas flow rate per unit area (m h

−1

)

g

gravity acceleration (=9.807 m s

−2

)

H

henry's law constant (atm or Pa kmol

−1

(or kg

−1

) m

3

)

H

height, height per transfer unit (m)

H

enthalpy (kJ)

H

s

height equivalent to an equilibrium stage (−)

Ht

hematocrit (%)

h

individual phase film coefficient of heat transfer (W m

−2

K

−1

or kcal h

−1

m

−2

°C

−1

)

J

mass transfer flux (kg or kmol h

−1

m

−2

)

J

F

filtrate flux (m s

−1

, m h

−1

, cm min

−1

, or cm s

−1

)

K

consistency index (g cm

−1

s

n−2

or kg m

−1

s

n−2

)

K

overall mass transfer coefficient (m h

−1

)

K

distribution coefficient, equilibrium constant (−)

K

m

michaelis constant (kmol m

−3

or mol cm

−3

)

K

p

proportional gain (−)

K

c

ultimate gain (−)

k

individual phase mass transfer coefficient (m h

−1

or cm s

−1

)

k

reaction rate constant (s

−1

, m

3

kmol

−1

s

−1

, etc.)

k

M

diffusive membrane permeability coefficient (m h

−1

or cm s

−1

)

L

length (m or cm)

L

v

volumetric liquid flow rate per unit area (m h

−1

)

m

partition coefficient (−)

N

mass transfer rate per unit volume (kmol or kg h

−1

m

−3

)

N

number of revolutions (s

−1

)

N

number of transfer unit (−)

N

number of theoretical plate (−)

N

i

number of moles of

i

component (kmol)

n

flow behavior index (−)

n

cell number (−)

O

output signal (−)

P

total pressure (Pa or bar)

P

power requirement (kJ s

−1

or W)

p

partial pressure (Pa or bar)

Q

heat transfer rate (kcal h

−1

or kJ s

−1

or W)

Q

total flow rate (m

3

s

−1

)

q

heat transfer flux (W m

−2

or kcal h

−1

m

−2

)

q

adsorbed amount (kmol kg

−1

)

R

gas law constant, 0.08206 atm l gmol

−1

K

−1

, (= 8.314 kJ kmol

−1

K

−1

, etc.)

R

hydraulic resistance in filtration (m

−1

)

R

,

r

radius (m or cm)

r

sphere-equivalent particle radius (m or cm)

r

i

reaction rate of

i

component (kmol m

−3

s

−1

)

RQ

respiratory quotient (−)

T

temperature (K)

T

I

integration time constant (s)

T

D

differential time constant (s)

T

temperature (°C or K)

t

time (s)

U

overall heat transfer coefficient (kcal h

−1

m

−2

°C

−1

or W m

−2

K

−1

)

U

superficial velocity (m s

−1

or cm s

−1

)

u

velocity (m s

−1

or cm s

−1

)

V

volume (m

3

)

V

max

maximum reaction rate (kmol m

−3

s

−1

)

v

velocity averaged over conduit cross section (m s

−1

or cm s

−1

)

v

t

terminal velocity (m s

−1

)

W

work done to system (kJ s

−1

or W)

W

mass flow rate per tube (kg s

−1

or g s

−1

)

W

peak width (m

3

or s)

w

weight (kg)

x

thickness of wall or membrane (m or cm)

x

mole fraction (−)

x

fractional conversion (−)

Y

xS

cell yield (kg dry cells/kg substrate consumed)

y

distance (m or cm)

y

oxygen saturation (% or −)

Δ

y

effective film thickness (m or cm)

Z

column height (m)

z

height of rectangular conduit of channel (m or cm)

Subscripts

G

gas

i

interface, inside, inlet

L

liquid

O

outside, outlet

0

initial

Superscripts

*

value in equilibrium with the other phase

Greek letters

α

thermal diffusivity (m

2

h

−1

or cm

2

s

−1

)

α

specific cake resistance (m kg

−1

)

γ

shear rate (s

−1

)

ϵ

void fraction (−)

ϵ

gas holdup (−)

ϵ

deviation (−)

φ

thiele modulus (−)

κ

thermal conductivity (W m

−1

K

−1

or kcal m

−1

h

−1

°C

−1

)

μ

viscosity (Pa s or g cm

−1

s

−1

)

μ

specific growth rate (h

−1

)

ν

kinematic viscosity =

μ

/

ρ

(cm

2

s

−1

or m

2

h

−1

)

ν

specific substrate consumption rate (g-substrate g-cell

−1

h

−1

)

Π

osmotic pressure (atm or Pa)

ρ

density (kg m

−3

)

ρ

specific product formation rate (g-product g-cell

−1

h

−1

)

σ

surface tension (kg s

−2

)

σ

reflection coefficient (−)

σ

standard deviation (−)

τ

shear stress (Pa)

τ

residence time (s)

ω

angular velocity (s

−1

)

Dimensionless numbers

(Bo) = (

g D

2

ρ

/

σ

)

bond number

(Da) = (−

r

a,max

/

k

L

A C

ab

)

damköhler number

(Fr) = [

U

G

/(

g D

)

1/2

]

froude number

(Ga) = (

g D

3

/

ν

2

)

galilei number

(Gz) = (

W c

p

/

κL

)

graetz number

(Nu) = (

h d

/

κ

)

nusselt number

(Nx) = (

F

/

D L

)

unnamed

(Pe) = (

v L

/

E

D

)

peclet number

(Pr) = (

c

p

μ

/

κ

)

prandtl number

(Re) = (

d v ρ

/

μ

)

reynolds number

(Sc) = (

μ

/

ρ D

)

schmidt number

(Sh) = (

k d

/

D

)

sherwood number

(St) = (

k

/

v

)

stanton number

Engineering can be defined as “the science or art of practical applications of the knowledge of pure sciences such as physics, chemistry, and biology.”

Compared with civil, mechanical, and other forms of engineering, chemical engineering is a relatively young branch of the subject that has been developed since the early twentieth century. The design and operation of efficient chemical plant equipment are the main duties of chemical engineers. It should be pointed out that industrial-scale chemical plant equipment cannot be built simply by enlarging the laboratory apparatus used in basic chemical research. Consider, for example, the case of a chemical reactor – that is, the apparatus used for chemical reactions. Although neither the type nor size of the reactor will affect the rate of chemical reaction per se, they will affect the overall or apparent reaction rate, which involves effects of physical processes, such as heat and mass transfer and fluid mixing. Thus, in the design and operation of plant-size reactor, knowledge of such physical factors – which is often neglected by chemists – is important.

G. E. Davis, a British pioneer in chemical engineering, described in his book, A Handbook of Chemical Engineering (1901, 1904), a variety of physical operations commonly used in chemical plants. In the United States, such physical operations as distillation, evaporation, heat transfer, gas absorption, and filtration were termed “unit operations” in 1915 by A. D. Little of the Massachusetts Institute of Technology (MIT), where the instruction of chemical engineering was organized via unit operations. The first complete textbook of unit operations entitled Principles of Chemical Engineering by Walker, Lewis, and McAdams of the MIT was published in 1923. Since then, the scope of chemical engineering has been broadened to include not only unit operations but also chemical reaction engineering, chemical engineering thermodynamics, process control, transport phenomena, and other areas.

Bioprocess plants using microorganisms and/or enzymes, such as fermentation plants, have many characteristics similar to those of chemical plants. Thus, a chemical engineering approach should be useful in the design and operation of various plants that involve biological systems, if differences in the physical properties of some materials are taken into account. Furthermore, chemical engineers are required to have some knowledge of biology when tackling problems that involve biological systems.

Since the publication of a pioneering textbook [1] in 1964, some excellent books [2, 3] have been produced in the area of the so-called biochemical or bioprocess engineering. Today, the applications of chemical engineering are becoming broader to include not only bioprocesses but also various biological systems involving environmental technology and even some medical devices, such as artificial organs.

A quantitative approach is important in any branch of engineering. However, this does not necessarily mean that engineers can solve everything theoretically, and quite often they use empirical rather than theoretical equations. Any equation – whether theoretical or empirical – that expresses some quantitative relationship must be dimensionally sound, as stated below.

In engineering calculations, a clear understanding of dimensions and units is very important. Dimensions are the basic concepts in expressing physical quantities. Dimensions used in chemical engineering are length (L), mass (M), time (T), the amount of substance (n), and temperature (θ). Some physical quantities have combined dimensions; for example, the dimensions of velocity and acceleration are L T−1 and L T−2, respectively. Sometimes, force (F) is also regarded as a dimension; however, as the force acting on a body is equal to the product of the mass of that body and the acceleration working on the body in the direction of force, F can be expressed as M L T−2.

Units are measures for dimensions. Scientists normally use the centimeter (cm), gram (g), second (s), mole (mol), and degree centigrade (°C) as the units for the length, mass, time, amount of substance, and temperature, respectively (the CGS (centimeter–gram–second) system), whereas the units often used by engineers are m, kg, h, kmol, and °C. Traditionally, engineers have used the kilogram as the unit for both mass and force. However, this practice sometimes causes confusion, and to avoid this, a designation of kilogram-force (kgf) is recommended. The unit for pressure, kg cm−2, often used by plant engineers should read kgf cm−2. Mass and weight are different entities; the weight of a body is the gravitational force acting on the body, that is, (mass) (gravitational acceleration g). Strictly speaking, g – and hence weight – will vary slightly with locations and altitudes on the Earth. It would be much smaller in a space ship.

In recent engineering research papers, units with the International System of Units (SI) are generally used. The SI system is different from the CGS system often used by scientists or from the conventional metric system used by engineers [4]. In the SI system, kilogram is used for mass only, and newton (N), which is the unit for force or weight, is defined as kg m s−2. The unit for pressure, Pa (pascal), is defined as N m−2. It is roughly the weight of an apple distributed over the area of 1 m2. As it is generally too small as a unit for pressure, kPa (kilopascal) (i.e., 1000 Pa), and MPa (megapascal) (i.e., 106 Pa) are more often used. One bar, which is equal to 0.987 atm, is 100 kPa = 0.1 MPa = 1000 hPa (hectopascal).

The SI unit for energy or heat is the joule (J), which is defined as J = N m = kg m2 s−2 = Pa m3. In the SI system, calorie is not used as a unit for heat, and hence no conversion between heat and work, such as 1 cal = 4.184 J, is needed. Power is defined as energy per unit time, and the SI unit for power is W (watt) = J s−1. Since W is usually too small for engineering calculations, kilowatt (=1000 W) is more often used. Although use of the SI units is preferred, we shall also use in this book the conventional metric units that are still widely used in engineering practice. The English engineering unit system is also used in engineering practice, but we do not use it in this text book. Values of the conversion factors between various units that are used in practice are listed in Appendix A, at the back of this book.

Empirical equations are often used in engineering calculations. For example, the following type of equation can relate the specific heat capacity cp (J kg−1 K−1) of a substance with its absolute temperature T (K).

1.1

where a (kJ kg−1 K−1) and b (kJ kg−1 K−2) are empirical constants. Their values in the kcal, kg, and °C units are different from those in the kJ, kg, and K units. Equations such as Equation 1.1 are called dimensional equations. The use of dimensional equations should preferably be avoided; hence, Equation 1.1 can be transformed to a nondimensional equation such as

1.2

where R is the gas law constant with the same dimension as cp and Tc is the critical temperature of the substance in question. Thus, as long as the same units are used for cp and R and for T and Tc, respectively, the values of the ratios in the parentheses as well as the values of coefficients a′ and b′ do not vary with the units used. Ratios such as those in the above parentheses are called dimensionless numbers (groups), and equations involving only dimensionless numbers are called dimensionless equations.

Dimensionless equations – some empirical and some with theoretical bases – are often used in chemical engineering calculations. Most dimensionless numbers are usually called by the names of person(s) who first proposed or used such numbers. They are also often expressed by the first two letters of a name, beginning with a capital letter; for example, the well-known Reynolds number, the values of which determine conditions of flow (laminar or turbulent) is usually designated as Re, or sometimes as NRe. The Reynolds number for flow inside a round straight tube is defined as dvρ/μ, in which d is the inside tube diameter (L), v is the fluid velocity averaged over the tube cross section (L T−1), ρ is the fluid density (M L−3), and μ is the fluid viscosity (M L−1 T−1) (this is defined in Chapter 2). Most dimensionless numbers have some significance, usually ratios of two physical quantities. How known variables could be arranged in a dimensionless number in an empirical dimensionless equation can be determined by a mathematical procedure known as dimensional analysis [5], which is not described in this text. Examples of some useful dimensionless equations or correlations appear in the following chapters of the book.

A pressure gauge reads 5.80 kgf cm−2. What is the pressure in SI units?

Let

It is important to distinguish between the intensive (state) properties (functions) and the extensive properties (functions).

Properties that do not vary with the amount of mass of a substance – for example, temperature, pressure, surface tension, mole fraction – are termed intensive properties. On the other hand, those properties that vary in proportion to the total mass of substances – for example, total volume, total mass, and heat capacity – are termed extensive properties.

It should be noted, however, that some extensive properties become intensive properties, in case their specific values – that is, their values for unit mass or unit volume – are considered. For example, specific heat (i.e., heat capacity per unit mass) and density (i.e., mass per unit volume) are intensive properties.

Sometimes, capital letters and small letters are used for extensive and intensive properties, respectively. For example, Cp indicates heat capacity (kJ °C−1) and cp specific heat capacity (kJ kg−1 °C−1). Measured values of intensive properties for common substances are available in various reference books [6].

Equilibria and rates should be clearly distinguished. Equilibrium is the end point of any spontaneous process, whether chemical or physical, in which the driving forces (potentials) for changes are balanced and there is no further tendency to change. Chemical equilibrium is the final state of a reaction at which no further changes in compositions occur at a given temperature and pressure. As an example of a physical process, let us consider the absorption of a gas into a liquid. When the equilibrium at a given temperature and pressure is reached after a sufficiently long time, the compositions of the gas and liquid phases cease to change. How much of a gas can be absorbed in the unit volume of a liquid at equilibrium – that is, the solubility of a gas in a liquid – is usually given by Henry's law:

1.3

where p is the partial pressure (Pa) of a gas, C is its equilibrium concentration (kg m−3) in a liquid, and H (Pa kg−1 m3) is the Henry's law constant, which varies with temperature. Equilibrium values do not vary with the experimental apparatus and procedure.

The rate of a chemical or physical process is its rapidity – that is, the speed of spontaneous changes toward the equilibrium. The rate of absorption of a gas into a liquid is the amount of the gas absorbed into the liquid per unit time. Such rates vary with the type and size of the apparatus, as well as its operating conditions. The rates of chemical or biochemical reactions in a homogeneous liquid phase depend on the concentrations of reactants, the temperature, the pressure, and the type and concentration of dissolved catalysts or enzymes. However, in the cases of heterogeneous chemical or biochemical reactions using particles of catalyst, immobilized enzymes or microorganisms, or microorganisms suspended in a liquid medium, and with an oxygen supply from the gas phase in case of an aerobic fermentation, the overall or apparent reaction rate(s) or growth rate(s) of the microorganism depend not only on chemical or biochemical factors but also on physical factors such as rates of transport of reactants outside or within the particles of catalyst or of immobilized enzymes or microorganisms. Such physical factors vary with the size and shape of the suspended particles, and with the size and geometry of the reaction vessel, as well as with operating conditions such as the degree of mixing or the rate(s) of gas supply. The physical conditions in industrial plant equipment are often quite different from those in the laboratory apparatus used in basic research.

Let us consider, as an example, a case of aerobic fermentation. The maximum amount of oxygen that can be absorbed into the unit volume of a fermentation medium at given temperature and pressure (i.e., the equilibrium relationship) is independent of the type and size of vessels used. On the other hand, the rates of oxygen absorption into the medium vary with the type and size of the fermentor and also with its operating conditions, such as the agitator speeds and rates of oxygen supply.

To summarize, chemical and physical equilibria are independent of the configuration of apparatus, whereas overall or apparent rates of chemical, biochemical, or microbial processes in industrial plants are substantially dependent on the configurations and operating conditions of the apparatus used. Thus, it is not appropriate to perform the so-called scaling-up using only those data obtained with a small laboratory apparatus.

Most chemical, biochemical, and physical operations in chemical and bioprocess plants can be performed batchwise or continuously.

A simple example is the heating of a liquid. If the amount of the fluid is rather small (e.g., 1 kl day−1), then batch heating is more economical and practical, with the use of a tank that can hold the entire liquid volume and is equipped with a built-in heater. However, when the amount of the liquid is fairly large (e.g., 1000 kl day−1), then continuous heating is more practical, using a heater in which the liquid flows at a constant rate and is heated to a required constant temperature. Most unit operations can be carried out either batchwise or continuously, depending on the scale of operation.

Most liquid phase chemical and biochemical reactions, with or without catalysts or enzymes, can be carried out either batchwise or continuously. For example, if the production scale is not large, then a reaction to produce C from A and B, all of which are soluble in water, can be carried out batchwise in a stirred tank reactor; that is, a tank equipped with a mechanical stirrer. The reactants A and B are charged into the reactor at the start of the operation. The product C is subsequently produced from A and B as time goes on, and can be separated from the aqueous solution when its concentration has reached a predetermined value.

When the production scale is large, the same reaction can be carried out continuously in the same type of reactor, or even with another type of reactor (Chapter 7). In this case, the supplies of the reactants A and B and the withdrawal of the solution containing product C are performed continuously, all at constant rates. The washout of the catalyst or enzyme particles can be prevented by installing a filter mesh at the exit of the product solution. Except for the transient start-up and finish-up periods, all the operating conditions such as temperature, stirrer speed, flow rates, and the concentrations of incoming and outgoing solutions remain constant – that is, in the steady state.

Material (mass) balance, the natural outcome from the law of conservation of mass, is a very important and useful concept in chemical engineering calculations. With usual chemical and/or biological systems, we need not consider nuclear reactions that convert mass into energy.

Let us consider a system that is separated from its surroundings by an imaginary boundary. The simplest expression for the total mass balance for the system is as follows:

1.4

The accumulation can be either positive or negative, depending on the relative magnitudes of the input and output. It should be zero with a continuously operated reactor mentioned in the previous section.

We can also consider the mass balance for a particular component in the total mass. Thus, for a component in a chemical reactor,

1.5

In mass balance calculations involving chemical and biochemical systems, it is sometimes more convenient to use the molar units, such as kilomoles, rather than simple mass units, such as the kilograms.

A flow of 2000 kg h−1 of aqueous solution of ethanol (10 wt% ethanol) from a fermentor is to be separated by continuous distillation into the distillate (90 wt% ethanol) and waste solution (0.5 wt% ethanol). Calculate the amounts of the distillate D (kg h−1) and the waste solution W (kg h−1).

Total mass balance:

Mass balance for ethanol:

From these relations, we obtain D = 212 kg h−1 and W = 1788 kg h−1.

Energy balance is an expression of the first law of thermodynamics – that is, the law of conservation of energy.

For a nonflow system separated from the surroundings by a boundary, the increase in the total energy of the system is given by

1.6

in which Q is the net heat supplied to the system and W is the work done by the system. Q and W are both energy in transit and hence have the same dimension as energy. The total energy of the system includes the total internal energy E, potential energy (PE), and kinetic energy (KE). In normal chemical engineering calculations, changes in (PE) and (KE) can be neglected. The internal energy E is the intrinsic energy of a substance including chemical and thermal energy of molecules. Although absolute values of E are unknown, ΔE, the difference from its base values, for example, from those at 0 °C and 1 atm, is often available or can be calculated.

Neglecting Δ(PE) and Δ(KE) we obtain from Equation 1.6

1.7

The internal energy per unit mass e is an intensive (state) function. Enthalpy h, a compound thermodynamic function defined by Equation 1.8, is also an intensive function.

1.8

in which p is the pressure and v is the specific volume. For a constant pressure process, it can be shown that

1.9

where cp is the specific heat at constant pressure.

For a steady-state flow system, again neglecting changes in the PEs and KEs, the energy balance per unit time is given by Equation 1.10.

1.10

where ΔH is the total enthalpy change, Q is the heat supplied to the system, and Ws is the so-called shaft work done by moving fluid to the surroundings, for example, work done by a turbine driven by a moving fluid.

In the second milk heater of a milk pasteurization plant 1000 l h−1 of raw milk is to be heated continuously from 75 to 135 °C by saturated steam at 500 kPa (152 °C). Calculate the steam consumption (kg h−1), neglecting heat loss. The density and specific heat of milk are 1.02 kg l−1 and 0.950 (kcal kg−1 °C−1), respectively.

Applying Equation 1.10 to this case, Ws is zero.

The heat of condensation (latent heat) of saturated steam at 500 kPa is given in the steam table as 503.6 kcal kg−1. Hence, steam consumption is 58 140/503.6 = 115.4 kg h−1.

1.1 What are the dimensions and SI units for the following physical quantities?

a. Pressure

b. Power

c. Heat capacity

1.2Is the following equation dimensionally sound?

where p is the atmospheric pressure, z is the height above the sea level, ρ is the specific density of air, and g is the gravity acceleration.

1.3 Convert the following units.

a. energy of 1 cm3 bar into J

b. a pressure of 25.3 lbf in−2 into SI units.

1.4 Explain the difference between mass and weight.

1.5 The Henry constant H′ = p/x for NH3 in water at 20 °C is 2.70 atm. Calculate the value of H = p/C, where C is kmol m−3, and m = y/x where x and y are the mole fractions in the liquid and gas phases, respectively.

1.6 It is required to remove 99% of CH4 from 200 m3 h−1 of air (1 atm, 20 °C) containing 20 mol% of CH4 by absorption into water. Calculate the minimum amount of water required (m3 h−1). The solubility of CH4 in water H′ = p/x at 20 °C is 3.76 × 104 atm.

1.7 A weight with a mass of 1 kg rests at 10 m above ground. It then falls freely to the ground. The acceleration of gravity is 9.8 m s−2. Calculate

a. the PE of the weight relative to the ground

b. the velocity and KE of the weight just before it strikes the ground.

1.8 100 kg h−1 of ethanol vapor at 1 atm, 78.3 °C is to be condensed by cooling with water at 20 °C. How much water will be required in the case where the exit water temperature is 30 °C? The heat of vaporization of ethanol at 1 atm, 78.3 °C is 204.3 kcal kg−1.

1.9 In the milk pasteurization plant of Example 1.3, what percentage of the heating steam can be saved, if a heat exchanger is installed to heat fresh milk at 75–95 °C by pasteurized milk at 132 °C?

1. Aiba, S., Humphrey, A.E., and Millis, N.F. (1964, 1973)

Biochemical Engineering

, University of Tokyo Press.

2. Lee, J.M. (1992)

Biochemical Engineering

, Prentice Hall.

3. Doran, P.M. (1995)

Bioprocess Engineering Principles

, Academic Press.

4. Oldeshue, J.Y. (1977)

Chem. Eng. Prog

.,

73

(8), 135.

5. McAdams, W.H. (1954)

Heat Transmission

, McGraw-Hill.

6. Perry, R.H., Green, D.W., and Malony, J.O. (eds) (1984, 1997)

Chemical Engineers' Handbook

, 6th and 7th edn, McGraw-Hill.

Hougen, O.A., Watson, K.M., and Ragatz, R.A. (1943, 1947, 1947)

Chemical Process Principles, Parts I, II, III

, John Wiley & Sons.

The role of physical transfer processes in bioprocess plants is as important as that of biochemical and microbial processes. Thus, knowledge of the engineering principles of such physical processes is important in the design and operation of bioprocess plants. Although this chapter is intended mainly for nonchemical engineers who are unfamiliar with such engineering principles, it might also be useful to chemical engineering students at the start of their careers.

In chemical engineering, the terms transfer of heat, mass, and momentum are referred to as the “transport phenomena.” The heating or cooling of fluids is a case of heat transfer, a good example of mass transfer being the transfer of oxygen from air into the culture media in an aerobic fermentor. When a fluid flows through a conduit, its pressure drops because of friction due to transfer of momentum, as shown later.

The driving forces, or driving potentials, for transport phenomena are (i) the temperature difference for heat transfer; (ii) the concentration or partial pressure difference for mass transfer; and (iii) the difference in momentum for momentum transfer. When the driving force becomes negligible, then the transport phenomenon will cease to occur, and the system will reach equilibrium.

It should be mentioned here that, in living systems the transport of mass sometimes takes place apparently against the concentration gradient. Such “uphill” mass transport, which usually occurs in biological membranes with the consumption of biochemical energy, is called “active transport,” and should be distinguished from “passive transport,” which is the ordinary “downhill” mass transport as discussed in this chapter. Active transport in biological systems is beyond the scope of this book.

Transport phenomena can take place between phases, as well as within one phase. Let us begin with the simpler case of transport phenomena within one phase, in connection with the definitions of transport properties.

Heat can be transferred by conduction, convection, or radiation and/or combinations thereof. Heat transfer within a homogeneous solid or a perfectly stagnant fluid in the absence of convection and radiation takes place solely by conduction. According to Fourier's law, the rate of heat conduction along the y-axis per unit area perpendicular to the y-axis (i.e., the heat flux q, expressed as W m−2 or kcal m−2 h−1) will vary in proportion to the temperature gradient in the y direction, dt/dy (°C m−1 or K m−1), and also to an intensive material property called heat or thermal conductivity κ (W m−1 K−1 or kcal h−1 m−1 °C−1). Thus,

2.1

The negative sign indicates that heat flows in the direction of negative temperature gradient, namely, from warmer to colder points. Some examples of the approximate values of thermal conductivity (kcal h−1 m−1 °C−1) at 20 °C are 330 for copper, 0.513 for liquid water, and 0.022 for oxygen gas at atmospheric pressure. Values of thermal conductivity generally increase with increasing temperature.

According to Fick's law, the flux of the transport of component A in a mixture of A and B along the y axis by pure molecular diffusion, that is, in the absence of convection, JA (kg h−1 m−2) is proportional to the concentration gradient of the diffusing component in the y direction, dCA/dy (kg m−4) and a system property called diffusivity or the diffusion coefficient of A in a mixture of A and B, DAB (m2 h−1 or cm2 s−1). Thus,

2.2

It should be noted that DAB is a property of the mixture of A and B, and is defined with reference to the mixture and not to the fixed coordinates. Except in the case of equimolar counter-diffusion of A and B, the diffusion of A would result in the movement of the mixture as a whole. However, in the usual case where the concentration of A is small, the value of DAB is practically equal to the value defined with reference to the fixed coordinates.

Values of diffusivity in gas mixtures at normal temperature and atmospheric pressure are in the approximate range of 0.03–0.3 m2 h−1 and usually increase with temperature and decrease with increasing pressure. Values of the liquid phase diffusivity in dilute solutions are in the approximate range of 0.2–1.2 × 10−5 m2 h−1, and increase with temperature. Both gas-phase and liquid-phase diffusivities can be estimated by various empirical correlations available in reference books.

There exists a conspicuous analogy between heat transfer and mass transfer. Hence, Equation 2.1 can be rewritten as

2.3

where cp is specific heat (kcal kg−1 °C−1), ρ is density (kg m−3), and α {= κ/(cpρ)} is the thermal diffusivity (m2 h−1), which has the same dimension as diffusivity.

The flow of fluid – whether gas or liquid – through pipes takes place in most chemical or bioprocess plants. There are two distinct regimes or modes of fluid flow. In the first regime, when all fluid elements flow only in one direction, and with no velocity components in any other direction, the flow is called laminar, streamline, or viscous flow. In the second regime, the fluid flow is turbulent, with random movements of the fluid elements or clusters of molecules occurring, but the flow as a whole is in one general direction. Incidentally, such random movements of fluid elements or clusters of molecules should not be confused with the random motion of individual molecules that causes molecular diffusion and heat conduction discussed in the previous sections, and also the momentum transport in laminar flow discussed below. Figure 2.1 shows, in a conceptual manner, the velocity profile in the laminar flow of a fluid between two large parallel plates moving at different velocities. If both plates move at constant but different velocities, with the top plate A at a faster velocity than the bottom plate B, a straight velocity profile such as shown in the figure will be established when steady conditions have been reached. This is due to the friction between the fluid layers parallel to the plates, and also between the plates and the adjacent fluid layers. In other words, a faster moving fluid layer tends to pull the adjacent slower moving fluid layer, and the latter tends to resist it. Thus, momentum is transferred from the faster moving fluid layer to the adjacent slower moving fluid layer. Therefore, a force must be applied to maintain the velocity gradient; such force per unit area parallel to the fluid layers τ (Pa) is called the shear stress. This varies in proportion to the velocity gradient du/dy (s−1), which is called the shear rate and is denoted by γ (s−1). Thus,

2.4

Figure 2.1 Velocity profile of laminar flow between parallel plates moving at different velocities.

The negative sign indicates that momentum is transferred down the velocity gradient. The proportionality constant μ (Pa s) is called molecular viscosity or simply viscosity, which is an intensive property. The unit of viscosity in CGS (centimeter–gram–second) units is called poise (g cm−1 s−1). From Equation 2.4 we obtain

2.5

which indicates that the shear stress; that is, the flux of momentum transfer varies in proportion to the momentum gradient and kinematic viscosity ν (= μ/ρ) (cm2 s−1 or m2 h−1). The unit (cm2 s−1) is sometimes called Stokes and denoted as St. This is Newton's law of viscosity. A comparison of Equations 2.3, and 2.5 indicates evident analogies among the transfer of mass, heat, and momentum. If the gradients of concentration, heat content, and momentum are taken as the driving forces in the three respective cases, the proportionality constants in the three rate equations are diffusivity, thermal diffusivity, and kinematic viscosity, respectively, all having the same dimension (L2 T−1) and the same units (cm2 s−1 or m2 h−1).

A fluid with viscosity that is independent of shear rates is called a Newtonian fluid. On a shear stress–shear rate diagram, such as Figure 2.2, it is represented by a straight line passing through the origin, the slope of which is the viscosity. All gases, and most common liquids of low molecular weights (e.g., water and ethanol) are Newtonian fluids. It is worth remembering that the viscosity of water at 20 °C is 0.01 poise (1 cp) in the CGS units and 0.001 Pa s in SI units. Liquid viscosity decreases with increasing temperature, whereas gas viscosity increases with increasing temperature. The viscosities of liquids and gases generally increase with pressure. Gas and liquid viscosities can be estimated by various equations and correlations available in reference books.

Figure 2.2 Relationships between shear rate and shear stress for Newtonian and non-Newtonian fluids.

Fluids that show viscosity variations with shear rates are called non-Newtonian fluids. Depending on how the shear stress varies with the shear rate, they are categorized into pseudoplastic, dilatant, and Bingham plastic fluids (Figure 2.2). The viscosity of pseudoplastic fluids decreases with increasing shear rate, whereas dilatant fluids show an increase in viscosity with shear rate. Bingham plastic fluids do not flow until a threshold stress called the yield stress is applied, after which the shear stress increases linearly with the shear rate. In general, the shear stress τ can be represented by Equation 2.6:

2.6

where K is called the consistency index and n is the flow behavior index. Values of n are smaller than 1 for pseudoplastic fluids, and >1 for dilatant fluids. The apparent viscosity μa (Pa s), which is defined by Equation 2.6, varies with shear rates (du/dy) (s−1); for a given shear rate, μa is given as the slope of the straight line joining the origin and the point for the shear rate on the shear rate–shear stress curve.

Fermentation broths – that is, fermentation medium containing microorganisms – often behave as non-Newtonian liquids, and in many cases their apparent viscosities vary with time, notably during the course of fermentation.

Fluids that show elasticity to some extent are termed viscoelastic fluids, and some polymer solutions demonstrate such behavior. Elasticity is the tendency of a substance or body to return to its original form, after the applied stress that caused strain (i.e., a relative volumetric change in the case of a polymer solution) has been removed. The elastic modulus (Pa) is the ratio of the applied stress (Pa) to strain (−). The relaxation time (s) of a viscoelastic fluid is defined as the ratio of its viscosity (Pa s) to its elastic modulus.

The following experimental data were obtained with use of a rotational viscometer for an aqueous solution of carboxylmethyl cellulose (CMC) containing 1.3 g CMC per 100 cm3 solution.

Shear rate d

u

/d

y

(s

−1

)

0.80

3.0

12

50

200

Shear stress

τ

(Pa)

0.329

0.870

2.44

6.99

19.6

Determine the values of the consistency index K, the flow behavior index n, and also the apparent viscosity μa at the shear rate of 50 s−1.

Taking the logarithms of Equation 2.6 we get

Thus, plotting the shear stress τ on the ordinate and the shear rate du/dy on the abscissa of a log–log paper gives a straight line (Figure 2.3), the slope of which is n